Resource Estimation for Quantum Variational Simulations of the Hubbard Model
Abstract
As the advances in quantum hardware bring us into the noisy intermediatescale quantum (NISQ) era, one possible task we can perform without quantum error correction using NISQ machines is the variational quantum eigensolver (VQE) due to its shallow depth. A specific problem that we can tackle is the strongly interacting FermiHubbard model, which is classically intractable and has practical implications in areas like superconductivity. In this paper, we outline the details about the gate sequence, the measurement scheme, and the relevant errormitigation techniques for the implementation of the Hubbard VQE on a NISQ platform. We perform resource estimation for both silicon spin qubits and superconducting qubits for a 50qubit simulation, which cannot be solved exactly via classical means, and find similar results. The number of twoqubit gates required is on the order of 20 000. Hence, to suppress the mean circuiterror count to a level such that we can obtain meaningful results with the aid of error mitigation, we need to achieve a twoqubit gate error rate of approximately 10^{4}. When searching for the ground state, we need a few days for one gradientdescent iteration, which is impractical. This can be reduced to around 10 min if we distribute our task among hundreds of quantumprocessing units. Hence, implementing a 50qubit Hubbard model VQE on a NISQ machine can be on the brink of being feasible in near term, but further optimization of our simulation scheme, improvements in the gate fidelity, improvements in the optimization scheme and advances in the errormitigation techniques are needed to overcome the remaining obstacles. The scalability of the hardware platform is also essential to overcome the runtime issue via parallelization, which can be done on one single silicon multicore processor or across multiple superconducting processors.
 Publication:

Physical Review Applied
 Pub Date:
 July 2020
 DOI:
 10.1103/PhysRevApplied.14.014059
 arXiv:
 arXiv:1910.02719
 Bibcode:
 2020PhRvP..14a4059C
 Keywords:

 Quantum Physics
 EPrint:
 Phys. Rev. Applied 14, 014059 (2020)